Two trolleys `A` and `B` are free to move on a level frictionless track, and are initially stationary. A man on trolley `A` throws a bag of mass `10 kg` with a horizontal velocity of `4 ms^(-1)` with respect to himself on to trolley `B` of mass `100 kg`. The combined mass of trolley `A` (excluding bag) and the man is `140 km`. Find the ratio of velocities of trolleys `A` and `B`, just after the bag lands on trolley `B`.

Explanation

Applying conservation principle of momentum for trolley `A` and bag

`mv-m_(1)v_(1)=0`
or `mv=m_(1)v_(1)`
or `10v=140v_(1)` …………..i
or `v=14v_(1)`
also, `v_(1)+v=4`
or `v_(1)+14v_(1)=4`
`:. v_(1)=4/15ms^(-1),v=14v_(1)=56/15ms^(-1)`
Applying conservation principle of momentum for bag and trolley
`B`
`mv=(m+m_(2))v_(2)`
`:. v_(2)=(mv)/(m+m_(2))=(10xx56/15)/110=56/(15xx11)`
`:. v_(1)/v_(2)=4/(15x56)=15xx11=11/14`